where Q is a real upper triangular matrix and \(\mathbf {x}\)  and its transpose \(\mathbf {x}^ are binary vectors.\) Most problems are not naturally expressed in the QUBO formulation, which requires the recasting of the problem.
Many problems have already been reformulated into the QUBO form [1]}.
For those problems that are not yet in such a list, techniques have been distilled to rewrite combinatorial optimization problems into the QUBO form [2]}.
The specific techniques used in this paper are: (1) including equality constraints, (2) including inequality constraints and (3) pairwise degree reduction.
